recent developments in high frequency financial ... - Index of

A multivariate integer count hurdle model 43
point t, t = 1,...,T. Such an approach enables us to verify whether the proposed
density specification is able to explain the whole conditional joint density of
the underlying data generating process. Relying on the simulated distributions at
every time point available, we can easily address this point applying the modified
version of the Diebold et al. (1998) density forecasting test for discrete data of
Liesenfeld et al. (2006).
Moreover, we are able to compare the residuals of both marginal processes.
We use here the standard sampling method proposed for Gaussian copula functions,
which can be summarized as:
For every t:
– Compute the Cholesky � �decomposition
Â(2×2) of estimated correlation matrix
ˆR, where ˆR
1 ˆρ
=
ˆρ 1
– Simulate xt = (x1t,x2t) ′ from a bivariate standard normal distribution
% Frequency
0 2 4 6 8 10 12 14
EUR/GBP EUR/USD
% Frequency
0 1 2 3 4 5 6 7 8
−40 −30 −20 −10 0 10 20 30 40 −40 −30 −20 −10 0 10 20 30 40
Category
Category
Fig. 8 Histogram of simulated tick changes of exchange rates.
Fig. 9 Bivariate histogram of the simulated tick changes of the EUR/GBP and the EUR/USD
exchange rates.